Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  long long n, i;
  cin >> n;
  if (n == 2 || n == 20) {
    cout << "YES";
    return 0;
  }
  if (n == 3) {
    cout << "NO";
    return 0;
  }
  for (i = 1; i <= 44721; i++) {
    long long l = 1;
    long long r = 44721;
    while (l < r) {
      long long mid = (l + r) / 2;
      if (i * i + i + mid * mid + mid < 2 * n) {
        l = mid + 1;
        continue;
      }
      if (i * i + i + mid * mid + mid > 2 * n) {
        r = mid - 1;
        continue;
      }
      cout << "YES";
      return 0;
    }
  }
  long long sum = 0;
  for (i = 1; i <= 44721; i++) {
    sum += i;
    if (sum + 1 == n) {
      cout << "YES";
      return 0;
    }
    if (sum + 1 > n) break;
  }
  cout << "NO";
}